Optics near Kerr black holes: spectra of advection dominated accretion flows

We investigate advection dominated accretion flows of matter in the vicinity of black holes, using the fully relativistic description in the frame of disk approximation. We also include some effects of the quasi-sphericity of the flow. We are interested in the spectra emitted by such flows and specifically, in the relativistic effects accompanying propagation of light. Using the ray shooting method in the Kerr metric we calculate the spectra of three different accretion flows. We also calculate the shape of a γ-ray line which could be formed in the flow, assuming that it has a natural Doppler profile. We find that effects of relativistic optics may influence the isotropy of the radiation and that observers close to the equatorial plane would measure a higher source luminosity. The line is strongly broadened, but the fact that the flow is quasi-spherical removes two-peak shape of the line characteristic for the spectra emitted from thin, Keplerian disks. The kinematics of the advection dominated flows is not unique (as opposed to Keplerian disks or spherical free-fall) and it would be probably difficult to find strong limits on source models using the spectral observations.